Question: Multiply and simplify the following complex numbers: $({-1+4i}) \cdot ({4-3i})$
Explanation: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-1+4i}) \cdot ({4-3i}) = $ $ ({-1} \cdot {4}) + ({-1} \cdot {-3i}) + ({4i} \cdot {4}) + ({4i} \cdot {-3i}) $ Then simplify the terms: $ (-4) + (3i) + (16i) + (-12i^2) $ Imaginary unit multiples can be grouped together. $ -4 + (3 + 16)i - 12 i^2 $ After we plug in $i^2 = -1$, the result becomes $ -4 + (3 + 16)i - (-12) $ The result is simplified: $ (-4 + 12) + (19i) = 8+19i $